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HACTEHA [7]
3 years ago
14

Please help me on this thanks! will giv brain liest if right.

Mathematics
1 answer:
egoroff_w [7]3 years ago
7 0

Answer:

10...?

Step-by-step explanation:

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The area of the shaded segment is 100cm^2. Calculate the value of r.
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Hello, 

The formula for finding the area of a circular region is: A=  \frac{ \alpha *r^{2} }{2}

then:
A_{1} = \frac{80*r^{2} }{2}

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cos(40)= \frac{h}{r}  \\  \\ h= r*cos(40)\\ \\ \\ sen(40)= \frac{b}{r} \\ \\ b=r*sen(40)

Now we can find its area:
A_{2}=2* \frac{b*h}{2}  \\  \\ A_{2}= [r*sen(40)][r*cos(40)]\\  \\A_{2}= r^{2}*sen(40)*cos(40)

The subtraction of the two areas is 100cm^2, then:

A_{1}-A_{2}=100cm^{2} \\ (40*r^{2})-(r^{2}*sen(40)*cos(40) )=100cm^{2} \\ 39.51r^{2}=100cm^{2} \\ r^{2}=2.53cm^{2} \\ r=1.59cm

Answer: r= 1.59cm
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3 years ago
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